Unimolecular decomposition of gases

The coUision theory of gaseous reactions requires two molecules to collide, suggesting that such reactions should be second-order. Many decompositions, e.g., N2O5, appear to be first-order at sufficiently high pressures of the gas. However, some such reactions do appear to be second-order at low gas pressure. In 1922, Lindemann proposed an explanation of these observations. 

Molecules transfer energy as a result of molecular collisions. Therefore, translational energy can be transferred to one molecule by another thereby 

The elementary reactions by which A is converted into products can be shown as 

In this scheme. A is the activated molecule of A. Although the process producing A is bimolecular, the decomposition of A is unimolecular. The change in [A] with time can be expressed by the equation 

Since A is an activated molecule, a reactive intermediate, the steady state approximation is assumed to apply (see Section 2.4). The rate of formation of A is assumed to be equal to its rate of decomposition. Therefore, 

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